Friday, December 5, 2014

3-Shot Groups

One of my brothers was lamenting his rifle's tendency to throw fliers. He knows that I have a little bit of background in using statistics to solve problems. So he asked if I had an opinion.

His groups looked like these. Click to embiggen.

He followed the advice given in many sporting magazines. He bought six different flavors of ammo and cranked out a three-shot group for each flavor. In many cases he would have two shots touching and a flier.

The spoiler

All of the groups illustrated above were generated with a 2" high zero at 100 yards and norm.inv function in Excel with a standard deviation of 0.5 inches. All groups were shot from a mathematically identical "rifle".

Most shooters would call this a one MOA gun based on 3-shot groups.

This is what roughly five hundred shots from the same rifle look like.

Using five, 3-shot groups was chosen as a benchmark. Bullets typically come on boxes of 20. That would leave five shots to harvest game. The median group size was chosen because it requires no calculation. Take your five measurements, discard the two largest groups and the two smallest groups and the one that is left is the median. Statisticians also favor using median values when analyzing scanty data because averages have no physical meaning if the data is bimodal.

Many thousands of simulations were run (as simple as pressing the f9 button). The 5/3-shot median method yielded a typical group size of 1.2" with lows of 0.7" and highs of 1.7" not uncommon. If your goal is to generate a group for bragging purposes, burning through five hundred rounds with this "rifle" would typically generate, by random chance, a minimum group that measured about 0.3". That same five hundred rounds would also typically generate a maximum group size in the neighborhood of 2.6".

Using a single 3-shot group to select the best ammo might be sufficient to sort out the very, very worst of the worst but does not contain enough information to discriminate between two populations with 50% difference in accuracy potential. Many groups with "fliers" is guaranteed when shooting three shot groups.

Good enough to shoot deer? You betchya! In fact, most hunters would have no trouble filling their tags with rifles that had one third of the intrinsic accuracy of this one.